- #1
paolorossi
- 24
- 0
Hello everybody,
I'm trying to understand if is possible to say something about the Floquet exponents, in the limit of a very slow changing on time. I try to explain. Given the differential equation
$$
\dot{\vec{v}}(t) = A(t) \vec{v}(t)
$$
with
$$
A(t+T)=A(t)
$$
a monodromy matrix is given by
$$
\Phi(T)
$$
where
$$\Phi(t)$$
is a matrix that is solution of
$$
\dot{\Phi}(t) = A(t) \Phi(t)
$$
and the Floquet exponents can be calculated from the spectrum of this monodromy matrix.
My question is:
can we calculate an expression for the Floquet exponents in terms of the eigenvalues of $$A(t)$$, in the limit $$T\rightarrow \infty$$ ?
I'm trying to understand if is possible to say something about the Floquet exponents, in the limit of a very slow changing on time. I try to explain. Given the differential equation
$$
\dot{\vec{v}}(t) = A(t) \vec{v}(t)
$$
with
$$
A(t+T)=A(t)
$$
a monodromy matrix is given by
$$
\Phi(T)
$$
where
$$\Phi(t)$$
is a matrix that is solution of
$$
\dot{\Phi}(t) = A(t) \Phi(t)
$$
and the Floquet exponents can be calculated from the spectrum of this monodromy matrix.
My question is:
can we calculate an expression for the Floquet exponents in terms of the eigenvalues of $$A(t)$$, in the limit $$T\rightarrow \infty$$ ?